This paper discusses some asymptotic uniform linearity results of randomly weighted empirical processes based on long range dependent random variables. These results are subsequently used to linearize nonlinear regression quantiles in a nonlinear regression model with long range dependent errors, where the design variables can be either random or nonrandom. These, in turn, yield the limiting behavior of the nonlinear regression quantiles. As a corollary, we obtain the limiting behavior of the least absolute deviation estimator and the trimmed mean estimator of the parameters of the nonlinear regression model. Some of the limiting properties are in striking contrast with the corresponding properties of a nonlinear regression model under independent and identically distributed error random variables. The paper also discusses an extension of rank score statistic in a nonlinear regression model.

This paper considers the problems of estimation and inference in the linear regression model with fractionally integrated errors. The ordinary least squares (OLS) and the first differenced (FD) estimators are studied. Relative to the OLS estimators, a substantial increase in the convergence rates of the coefficient estimator for the stochastic regressor can be achieved by the FD estimators when the error term is nonstationary. However, the preceding decisive results can not always sustain when the error term is stationary. We also find that the FD estimators can eliminate the spurious regression because the FD t-ratio for the coefficient estimators never diverges.

This study investigates the effects of varying sampling intervals on the long memory characteristics of certain stochastic processes. We find that although different sampling intervals do not affect the decay rate of discrete time long memory autocorrelation functions in large lags, the autocorrelation functions in short lags are affected significantly. The level of the autocorrelation functions moves upward for temporally aggregated processes and downward for systematically sampled processes, and these effects result in a bias in the long memory parameter. For the ARFIMA(0,d,0) process, the absolute magnitude of the long memory parameter, |d|, of the temporally aggregated process is greater than the |d| of the true process, which is greater than the |d| of the systematically sampled process. We also find that the true long memory parameter can be obtained if we use a decay rate that is not affected by different sampling intervals.

Testing the cointegrating rank of a vector autoregressive process with an intercept is considered. In addition to the likelihood ratio (LR) tests developed by Johansen and Juselius (1990, Oxford Bulletin of Economics and Statistics, 52, 169–210) and others we also consider an alternative class of tests that is based on estimating the trend parameters of the deterministic term in a different way. The asymptotic local power of these tests is derived and compared to that of the corresponding LR tests. The small sample properties are investigated by simulations. The new tests are seen to be substantially more powerful than conventional LR tests.

In this paper I present an alternative derivation of the asymptotic distribution of Kremers, Ericsson, and Dolado's (1992, Oxford Bulletin of Economics and Statistics 54, 325–348) conditional error correction model (ECM)–based t-test for cointegration with a single prespecified cointegrating vector. This alternative distribution, which is identical to the distribution of Hansen's (1995, Econometric Theory 11, 1148–1171) covariate augmented t-test for a unit root, is valid for weakly exogenous regressors and depends on a consistently estimable nuisance parameter that takes on values in the unit interval. I show analytically, using asymptotic power functions based on near-cointegrated alternatives, that the ECM t-test with a prespecified cointegrating vector can have much higher power than single equation tests for cointegration based on estimating the cointegrating vector. I also characterize situations in which the ECM t-test computed with a misspecified cointegrating vector will have high power.

The prediction of future events and developments is an exciting and perhaps mysterious task, often associated with the aura of prophets and seers instead of probabilistic models and computer screens. The reality of macroeconomic forecasting, however, is quite mundane. Predictions of macroeconomic aggregates play an important role in the decision making of private enterprises, central banks, and governments. In general, forecasts become less popular if they turn out to be inaccurate ex post, and the postwar history of macroeconomic forecasting has had its share of disappointments. For instance, in the early 1980's, economists tested inflation forecasts taken over the previous 20 years and found that the forecasts were poor, partly as a result of the oil price shocks in the 1970's. A recent study (Croushore, 1998) with data up to 1996 provides a more favorable assessment of the quality of inflation forecasts.